Representative democracy sucks, it just sucks less than everything else we’ve tried. Plebiscites on specific issues are terrible: that’s how we got Brexit and woke up the next day astonished that our neighbors had been so daft.
Brexit is an interesting case to bring up. As someone who voted against it, it is also clear to me that it hasn't been implemented in any way that could have made it a success from the representatives, and looks like a clear case of the representatives maliciously complying with a decree that they didn't agree with.
I remain unconvinced that we can't do better than a system of government that is over 200 years old that only exists as a function of the technology at the time.